here’s how the game works for a 3×3-box grid that i’ve played already:
there’s an inventory of 9 symbols. you have to put one symbol in each box once.
each symbol represents a speech sound or phoneme. that point doesn’t really matter as far as design is concerned, except to understand that, for the purposes of the game, each symbol can be said to have two defining features or attributes: PLACE of articulation (where in your mouth is this happening) and MANNER of articulation (which basically means what kind of sound is it).
an example inventory, with PLACE on the X axis and MANNER on the Y axis:
** another way of thinking about it is that each symbol is really like a shorthand way of saying “a thing with attributes X and Y”. **
in the above puzzle, i can see that the open cell in the top row cannot be alveolar or velar for PLACE (X axis on the inventory) and can’t be nasal or plosive for MANNER (Y axis on the inventory), so by process of elimination i know it has to be the bilabial (PLACE) fricative (MANNER).
so the long and short of that is: for each of the 9 symbols, you have two attributes that help you identify what it is
(or, the reverse: if you know a given square must contain one or more specific attributes, you can narrow down or immediately identify what symbol it must be).
rules: all the symbols are used once; no row or column may contain more than one symbol with either the same place or same manner of articulation.
i’ll use the sound “b” to convert this to a literal example. its two attributes are:
1 (manner): it’s a hard consonant (aka plosive)
2 (place): it’s made with both lips (aka bilabial)
so if i determine by process of elimination that a given box needs to have exactly those two attributes, i know it has to be the symbol [b] that goes there. or if i can only determine, say, that it has to be something that’s bilabial, then i’ve at least narrowed down the possible choices to 3.
… ok, got that?
so this above-described version seems simple enough that it seems relatively easy to algorithm-ize. and i’d like to do so. and if that’s all that’s feasible, that’s fine.
but what i’m even more interested in, and less sure about, is adding additional layers of difficulty.
so now i’ll turn to the fancier, bigger-grid version, which i will outline below:
a 4×4 grid. 16 symbols.
same rules — no row or column may contain more than one symbol with either of the same attributes. but this version has an additional constraint: the four sub-squares (2×2) are also not allowed to contain more than one symbol with either the same place or same manner of articulation.
ok, now here’s the tricky bit. with this version, instead of just being given a couple symbols to get you started, you get:
– a couple squares that contain symbols like normal (aka you are told both attributes)
– a couple squares where you are given only one attribute. example:
this adds a delicious level of challenge. where i stumble is trying to imagine how this additional layer of difficulty could be built.
example phoneme inventory for 4×4 version (still with PLACE on the X axis and MANNER on the Y axis):
… and then there’s an EVEN CRAZIER version but i’ll stop there.